Applications are now being accepted from people who would like to live at 135 Lafayette, the housing development under construction at the former St. Joseph Church site.

The affordable housing complex is slated to be finished and occupied by January 2014. Applications to live in the building’s 51 one-, two- and three-bedroom apartments are due by Sept. 19, and a lottery will be held to select tenants on Sept. 26.

“Things are on track. We’re making very good progress,” said Lisa Alberghini, president of the Planning Office for Urban Affairs, a developer affiliated with the Archdiocese of Boston. “We’re expecting construction to be completed around the end of the year.”

The 63-year-old St. Joseph Church building was demolished this winter. It had sat vacant for nine years, after the parish was closed by the archdiocese. Construction of the four-story building began soon after the church was demolished.

The Planning Office for Urban Affairs, which owns the property, has hired Peabody Properties to manage the housing application and lo

“We are getting a lot of interest,” Alberghini said. “We’re very excited about it. We’ve been in touch with a lot of the neighborhood re

sidents, and they seem equally excited to see that stretch (of Lafayette Street) reinvigorated.

“We’re just really thrilled to be here.”

Alberghini said that they are continuing to explore options for a first-floor retail or community space in the Lafayette building.

Units are set aside for applicants who make 30, 50 and 60 percent of the area’s median income. For a two-person household, a 30 percent income would be $22,650; 50 percent would be $37,800; and 60 percent would be $45,360 (based on 2012 averages).

Rents will vary based on income. Eight units are set aside as Section 8 affordable housing for tenants who make 30 percent of the median income.

A spokesperson from Peabody Properties familiar with the project was out of the office Friday and unavailable for comment.

On its website, 135Lafayetteapts.com, the company describes the property as a “mixed-income rental community of 51 affordable one, two and three-bedroom apartment homes … at the center of Salem’s trendiest downtown.”

“135 Lafayette offers a varied selection of floor plans, providing open and flexible living spaces with abundant natural light and warm, inviting interiors.”

Bethany Bray can be reached at bbray@salemnews.com and on Twitter @SalemNewsBB